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Integral models of representations of current groups. (English) Zbl 1162.22019
Funct. Anal. Appl. 42, No. 1, 19-27 (2008); translation from Funkts. Anal. Prilozh. 42, No. 1, 22-32 (2008).
Authors’ summary: We suggest a new construction of nonlocal representations of the current group. Instead of the Fock space, which is usually used in this situation, we consider the direct integral of countable tensor products of representations over the trajectories of some stochastic process. The construction substantially uses the invariance of the so-called infinite-dimensional Lebesgue measure.

MSC:
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
22E67 Loop groups and related constructions, group-theoretic treatment
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